Abstract: Abstract: This study establishes a central limit theorem (CLT) for R 2 statistics in a moderately high-dimensional asymptotic framework. The underlying population accommodates a general independent components model, by which our result unifies two existing CLTs. Beyond this, the new CLT characterizes the effect of kurtosis of the latent independent components on the fluctuation of R 2 statistics. As an application, a novel confidence interval is constructed for the coefficient of multiple correlation in a high-dimensional linear regression.
Key words and phrases: High dimension, independent components model, multiple correlation coefficient.